Math Techniques of Calculus I Penn State University Summer Session 2017

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1 Math Techniques of Calculus I Penn State University Summer Session 2017 Instructor: Sergio Zamora Barrera Office: 018 McAllister Bldg Office phone: Office Hours: M-F 11:00-12:00 Class Time and Location: Willard Bldg 265, M-F, 09:35-10:10. Policy: s sent to me will be replied in less than 48 hours. Course Description: Functions, graphs, derivatives, integrals, techniques of differentiation and integration. Applications to business, economics and social and life sciences. Students may take only one course for credit from MATH 110, 140, 140A, and 140B. Prerequisite: MATH 022 or satisfactory performance on the mathematics proficiency examination. Course Coverage: The goal for the course is to cover the chapters/sections detailed in the tentative class schedule below. Those include most of the contents of chapters 1-6 from the textbook. Textbook: Calculus for Business, Economics, and the Social and Life Sciences, Brief Edition, Tenth Edition. Hoffman, Bradley. McGraw Hill. Tentative Class Schedule (Lectures) Section Date Contents 1.1, /12 Functions and Graphs /13 Linear Functions /14 Functional Models /15 Limits /16 One Sided Limits and Continuity 06/19 Applications

2 Section Date Contents /20 The Derivative /21 Techniques of Derivation /22 Higher Order Derivatives /23 The Chain Rule /26 Marginal Analysis and Approximations /27 Implicit Differentiation 06/28 Applications 06/29 Review Quiz 1 06/30 Chapters 1 and /03 Monotone Functions and Relative Extrema /05 Concavity and Points of Inflection /06 Curve Sketching /07 Optimization and Elasticity of Demand /10 Applied Optimization 07/11 Applications /12 Exponential Functions, Continuous Compounding /13 Logarithmic Functions /14 Differentiation of Exponential and Logarithmic Functions /17 Exponential Models 07/18 Applications 07/19 Review Quiz 2 07/20 Chapters 3 and /21 Indefinite Integral /24 Integration by Substitution /25 Definite Integral and Fundamental Theorem of Calculus /26 Applications /27 Applications /28 Applications /31 Integration by Parts /01 Differential Equations /02 Improper Integrals /03 Numerical Integration 08/04 Applications 08/07 Applications 08/08 Review Final Quiz 08/09 Chapters 5 and 6

3 Learning Objectives: Upon successful completion of Math 110, the student should be able to: 1. Identify polynomial, rational, power, exponential, and logarithmic functions. 2. Calculate the domains of polynomial, rational, power, exponential, and logarithmic functions. 3. Calculate the sums, differences, products, quotients, and compositions of functions. 4. Model cost, revenue, profit, supply, and demand business functions. 5. Calculate equilibrium points within supply/demand markets and interpret the results. 6. Calculate or estimate finite/infinite limits of functions given by formulas, graphs, or tables. 7. Calculate one-sided limits of functions. 8. Determine whether a function given by a graph or formula is continuous at a given point or on a given interval. 9. Determine whether a function given by a graph or formula is differentiable at a given point or on a given interval. 10. Distinguish between average and instantaneous rate of change and interpret the definition of the derivative graphically.

4 11. Determine derivatives of some functions using the definition of derivative of a function. 12. Calculate derivatives of polynomial, rational, power, exponential, and logarithmic functions, and combinations of these functions. 13. Calculate derivatives of implicitly defined functions. 14. Apply the ideas and techniques of derivatives to related rate problems to include basic algebraic/geometric models and cost/average cost, revenue/average revenue, profit/average profit, supply, and demand models. 15. Apply the ideas and techniques of derivatives to perform marginal analysis of basic economics models. 16. Apply the ideas and techniques of derivatives to calculate elasticity of basic economics models. 17. Apply the ideas and techniques of derivatives to determine intervals where a models/graph is: a) Increasing/decreasing. b) Concave up/down. 18. Apply the ideas and techniques of derivatives to determine points in a model/graph that are: a) Relative extrema. b) Absolute extrema.

5 c) Critical Values. d) Points of Inflection. 19. Identify vertical and horizontal asymptotic. 20. Apply the ideas and techniques of derivatives to graphing or recognizing the graphs of functions. 21. Apply the ideas and techniques of derivatives to optimization problems to include basic algebraic/geometric models and cost, revenue, profit, supply, and demand models. 22. Apply the ideas and techniques of derivatives to solve: a) Compound interest. b) Continuous interest. c) Effective interest rate. d) Present value business models. 23. Determine the point-of-diminishing returns for a model/function. 24. Calculate the derivatives of functions using logarithmic differentiation. 25. Calculate the Riemann sum for a given function, partition and collection of evaluation points. 26. Describe a definite integral as the limit of a Riemann sum.

6 27. Determine anti-derivatives of basic algebraic functions. 28. Calculate values of definite integrals using anti-derivatives and areas. 29. Apply concepts of integration to solving basic business model applications. 30. Apply substitution and integration by parts techniques to integrate basic functions. 31. Apply the ideas of definite integrals to solve problems of areas. 32. Calculate the average value of business models using the definite integral. 33. Apply the ideas and techniques of the definite integral to evaluate: a) Consumer/producer surplus. b) Future/present value of income streams. c) Future/present value of annuities business models. 34. Evaluate improper integrals and apply the ideas and techniques to evaluate perpetuities. Grading policy: Grades will be assigned on the basis of 1300 points distributed as follows: Homework 600 Quiz Quiz Final Quiz 300 Total 1300

7 Final course grades will be assigned using the following criteria: Grade Minimum Score Percent A B B B C C C D D D F 0 0 Your grade will be based exclusively on homework and quizzes. There is no extra-credit work. Academic Integrity: Academic integrity is the pursuit of scholarly activity in an open, honest and responsible manner. Academic integrity is a basic guiding principle for all academic activity at The Pennsylvania State University, and all members of the University community are expected to act in accordance with this principle. Consistent with this expectation, the University s Code of Conduct states that all students should act with personal integrity, respect other students dignity, rights and property, and help create and maintain an environment in which all can succeed through the fruits of their efforts. Academic integrity includes a commitment not to engage in or tolerate acts of falsification, misrepresentation or deception. Such acts of dishonesty violate the fundamental ethical principles of the University community and compromise the worth of work completed by others. In order to ensure all students have a fair and equal opportunity to succeed in this course, the Math Department is committed to enforcing the University s academic integrity policy. Below is a description of academic misconduct and the department s responsibilities when misconduct is suspected.

8 Academic Misconduct: I this course academic misconduct includes, but is not limited to: 1. Copying the work of another student, on an exam, quiz or assignment. 2. Passing off the work of another individual as your own. 3. Using non-approved devices or aids on exams, quizzes or assignments. 4. Having unauthorized possession of exams or quizzes. 5. Engaging in deception in order to extend or reschedule an exam, quiz or assignment. 6. Facilitating acts of academic misconduct by others. When Academic Misconduct is Suspected: If a student is suspected of academic misconduct, the instructor s duties are to: 1. Confidentially inform the student of the allegation. 2. Enter the charge and recommended sanctions on an Eberly College or Science Academic Integrity form. 3. Ask the student to meet in order to review the form and discuss the charge and sanctions. The student can choose to accept or contest the allegation at this point. Note that a student s refusal to meet with the instructor or respond to the charges within a reasonable period of time is construed as acceptance of the allegation and proposed sanctions.

9 Once the Academic Integrity form has been accepted or contested by the student, it is sent to the College s Academic Integrity Committee for adjudication. A student cannot drop or withdraw from the course during the adjudication process. Sanctions: If a student accepts an academic misconduct allegation, or if (s)he is found guilty during adjudication, probable sanctions include: 1. A warning. 2. Reduction of the assignment grade to zero or Reduction of the quiz or exam grade to zero. Additional sanctions might include: 1. Reduction in the final course grade. 2. An F in the course. In addition, the student will be unable to drop or withdraw fro the course. Please see the Eberly College of Science Academic Integrity homepage for additional information and procedures: Students with disabilities: Penn State welcomes students with disabilities into the University s educational programs. If you have a disability related need for reasonable academic adjustments in this course, contact Student Disability Resources at (V/TTY). For further information, please visit Student Disability Resources web site: In order to receive consideration for accommodations, you must contact SDR and provide documentation (see the documentation guidelines at disability-resources/). If the documentation supports your request for reasonable accommodations, SDR will provide you with an accommodation letter identifying appropriate

10 academic adjustments. Please share this letter with your instructors and discuss the accommodations with them as early in your courses as possible. You must follow this process for every semester that you request accommodations.

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